A187262 -id:A187262 - cp's OEIS frontend

A187106 Number of nonempty subsets of {1, 2, ..., n} having pairwise coprime elements.

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 495, 543, 615, 727, 1455, 1519, 3039, 3231, 3615, 3871, 7743, 7999, 11167, 11903, 14655, 15487, 30975, 31231, 62463, 69887, 76159, 80255, 89855, 91647, 183295, 192639, 208639, 214271, 428543

Offset: 1

Alois P. Heinz, Mar 06 2011

nonn

			a(4) = 11 because there are 11 nonempty subsets of {1,2,3,4} having pairwise coprime elements: {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,3,4}.

Alois P. Heinz, Table of n, a(n) for n = 1..220

Cf. A036234. Row sums of triangle A186974. Partial sums of A186973. Rightmost elements in rows of triangle A187262.

Cf. A084422.

f(n,k=1)=if(n==1, return(2)); if(gcd(k,n)==1, f(n-1,n*k)) + f(n-1,k)
a(n)=f(n)-1 \\ Charles R Greathouse IV, Aug 24 2016

a(n) = Sum_{k=1..A036234(n)} A186974(n,k).
a(n) = Sum_{i=1..n} A186973(i).
a(n) = A187262(n,A036234(n)).
a(n) = A084422(n) - 1.

A187263 Number of nonempty subsets of {1, 2, ..., n} with <=2 pairwise coprime elements.

Original entry on oeis.org

1, 3, 6, 9, 14, 17, 24, 29, 36, 41, 52, 57, 70, 77, 86, 95, 112, 119, 138, 147, 160, 171, 194, 203, 224, 237, 256, 269, 298, 307, 338, 355, 376, 393, 418, 431, 468, 487, 512, 529, 570, 583, 626, 647, 672, 695, 742, 759, 802, 823

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

			a(4) = 9 because there are 9 nonempty subsets of {1,2,3,4} with <=2 pairwise coprime elements: {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Column 2 of triangle A187262. First differences are A039649 for n>1.

a(n) = A187262(n,2).

A187264 Number of nonempty subsets of {1, 2, ..., n} with <=3 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 21, 25, 43, 54, 73, 83, 125, 136, 194, 215, 245, 278, 374, 396, 516, 552, 614, 662, 834, 871, 1018, 1087, 1215, 1285, 1555, 1592, 1900, 2023, 2181, 2298, 2506, 2581, 3013, 3160, 3378, 3497, 4027, 4105, 4689, 4875, 5103

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

			a(4) = 11 because there are 11 nonempty subsets of {1,2,3,4} with <=3 pairwise coprime elements: {1}, {2}, {3}, {4}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,3,4}.

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Column 3 of triangle A187262. First differences are A186987.

a(n) = A187262(n,3).

A187265 Number of nonempty subsets of {1, 2, ..., n} with <= 4 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 53, 68, 97, 109, 193, 208, 345, 382, 437, 506, 785, 827, 1224, 1310, 1472, 1590, 2253, 2346, 2892, 3100, 3568, 3784, 5070, 5163, 6756, 7277, 7928, 8387, 9301, 9560, 12142, 12790, 13815, 14297, 17795, 18083, 22189

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

			a(5) = 23 because there are 23 nonempty subsets of {1,2,3,4,5} with <=4 pairwise coprime elements: {1}, {2}, {3}, {4}, {5}, {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,5}, {3,4}, {3,5}, {4,5}, {1,2,3}, {1,2,5}, {1,3,4}, {1,3,5}, {1,4,5}, {2,3,5}, {3,4,5}, {1,2,3,5}, {1,3,4,5}.

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Column 4 of triangle A187262. First differences are A186988.

a(n) = A187262(n,4).

A187266 Number of nonempty subsets of {1, 2, ..., n} with <=5 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 225, 241, 450, 496, 565, 663, 1170, 1227, 2055, 2196, 2473, 2666, 4257, 4420, 5709, 6122, 7223, 7664, 11449, 11612, 16776, 18255, 19991, 21178, 23718, 24327, 33888, 35767, 38853, 40157, 54455

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 5 of triangle A187262. First differences are A186989.

a(n) = A187262(n,5).

A187267 Number of nonempty subsets of {1, 2, ..., n} with <=6 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 489, 537, 609, 719, 1383, 1446, 2674, 2851, 3204, 3443, 6110, 6329, 8484, 9083, 10930, 11587, 19252, 19471, 31084, 34131, 37428, 39637, 44583, 45640, 69968, 73870, 80421, 82985

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 6 of triangle A187262. First differences are A186990.

a(n) = A187262(n,6).

A187268 Number of nonempty subsets of {1, 2, ..., n} with <=7 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 495, 543, 615, 727, 1447, 1511, 2958, 3148, 3528, 3782, 7226, 7473, 10268, 10969, 13379, 14163, 25751, 25998, 45470, 50309, 55111, 58286, 65586, 67035, 112676, 118867, 129387, 133295

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 7 of triangle A187262. First differences are A186991.

a(n) = A187262(n,7).

A187269 Number of nonempty subsets of {1, 2, ..., n} with <=8 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 495, 543, 615, 727, 1455, 1519, 3031, 3223, 3607, 3863, 7646, 7901, 10987, 11719, 14393, 15219, 29383, 29638, 55637, 61912, 67681, 71466, 80284, 81965, 149001, 156985, 170628

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 8 of triangle A187262. First differences are A186992.

a(n) = A187262(n,8).

A187270 Number of nonempty subsets of {1, 2, ..., n} with <=9 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 495, 543, 615, 727, 1455, 1519, 3039, 3231, 3615, 3871, 7735, 7991, 11151, 11887, 14631, 15463, 30683, 30939, 60578, 67646, 73813, 77845, 87284, 89054, 171020, 179960, 195265

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 9 of triangle A187262. First differences are A186993.

a(n) = A187262(n,9).

A187271 Number of nonempty subsets of {1, 2, ..., n} with <=10 pairwise coprime elements.

Original entry on oeis.org

1, 3, 7, 11, 23, 27, 55, 71, 103, 115, 231, 247, 495, 543, 615, 727, 1455, 1519, 3039, 3231, 3615, 3871, 7743, 7999, 11167, 11903, 14655, 15487, 30951, 31207, 62147, 69503, 75765, 79855, 89440, 91230, 180285, 189556, 205432

Offset: 1

Alois P. Heinz, Mar 07 2011

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..200

Column 10 of triangle A187262.

a(n) = A187262(n,10).

cp's OEIS Frontend

A187106 Number of nonempty subsets of {1, 2, ..., n} having pairwise coprime elements.

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A187263 Number of nonempty subsets of {1, 2, ..., n} with <=2 pairwise coprime elements.

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A187264 Number of nonempty subsets of {1, 2, ..., n} with <=3 pairwise coprime elements.

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A187265 Number of nonempty subsets of {1, 2, ..., n} with <= 4 pairwise coprime elements.

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A187266 Number of nonempty subsets of {1, 2, ..., n} with <=5 pairwise coprime elements.

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A187267 Number of nonempty subsets of {1, 2, ..., n} with <=6 pairwise coprime elements.

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A187268 Number of nonempty subsets of {1, 2, ..., n} with <=7 pairwise coprime elements.

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A187269 Number of nonempty subsets of {1, 2, ..., n} with <=8 pairwise coprime elements.

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Formula

A187270 Number of nonempty subsets of {1, 2, ..., n} with <=9 pairwise coprime elements.

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Keywords

Links

Crossrefs

Formula

A187271 Number of nonempty subsets of {1, 2, ..., n} with <=10 pairwise coprime elements.

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Author

Keywords

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Formula